Question

Ice cream is filled to the brim in a cylindrical container of radius 20 cm and height 60 cm. How many cones of radius 3 cm and height 10 cm are needed to hold this ice cream?

Answer 1

Radius of the cylindrical container in which ice cream is filled = 20 cm
Height of the cylindrical container in which ice cream is filled = 60 cm
Volume of a cylinder = πr²h
= π × 20 × 20 × 60
= 24000 π cm³

Radius of each cone in which this ice cream is to be transferred = 3 cm
Height of each cone in which this ice cream is to be transferred = 10 cm
Volume of a cone =$\frac{1}{3}\mathrm{\pi }{r}^{2}h$
= $\frac{1}{3}$ π × 3 × 3 × 10
= 30 π cm³
Volume of each cone in which this ice cream is to be transferred = 30 π cm³
Let the number of cones required be n.
The volume of the cylinder will be equal to the collective volume of all the cones.
∴ 30 π × n = 24000 π
⇒ n = 800
∴ The number of cones required = 800